Hi I have images of 8 lion overstamped on a previous initial mark, all from the same die, the 'clearest image is of the Roger Shuttlewood coin which was described as Lion over portcullis and as such was described in my book on the threepence. Your example ( from the same dies ) does show a clearer mark which looks to be a rose rather than portcullis. For the reverse dies there are 4 dies with lion over portcullis and dated 1566 in these cases it is lion over portcullis. There is a unique reverse found in the National Museum of Liverpool which has a 1566/5 with rose initial mark but this has a normal 1565 rose initial mark obverse. Given the vast range of overstamping of dies during the 1560-1581 period it is not unlikely that a rose initial mark die of 1565 was overstamped with a lion.
1566 lion over portcullis( Rose) obv
British Museum (1), C,.Coomber (1), DIG (3), W. Wilkinson (1), R Shuttlewood (1) and one specimen(which probably is the above ) ex M Rassmussen 2010[ Catalogue photo not very clear)